Negative influence suppression maximization method in group network considering budget constraint

Abstract

The invention discloses a method for maximizing negative influence suppression in a group network considering budget constraint in the technical field of information social networks, which comprises the following steps: step 1, establishing a GIC model; step 2, defining cost limitation: node cost and group composition; 3, designing a negative information suppression maximization algorithm fusing multiple strategies under cost limitation, wherein the negative information suppression maximization algorithm comprises group composition cost income, group infection rate and group connection scale; step 4, selecting positive seeds; the method comprises the following steps: establishing a group independent cascade model, simulating the propagation dynamic state of information under a group structure, designing a negative information suppression maximization algorithm fusing multiple strategies under cost limitation, and selecting an optimal suppression strategy by comprehensively considering factors such as cost effectiveness, a group infection rate and a group connection scale; therefore, effective suppression of negative information spreading is realized under limited budget.

Description

Technical Field

[0001] The present invention relates to a method for maximizing negative influence suppression in a group network considering budget constraints in the technical field of information social network. Background Art

[0002] In recent years, with the rapid development of online social networks, the speed and scope of information dissemination have significantly increased. However, the rapid spread of negative information (such as rumors and fake news) has also posed numerous challenges to society. Group structures are a common and important feature of social networks. For example, on platforms such as WeChat, Weibo, and forums, users not only establish "follow-follow" relationships but also receive group messages by joining various groups. Therefore, in social networks, information dissemination depends not only on direct connections between nodes but is also influenced by group structure. Information dissemination within groups is broadcast-like; even if nodes are not directly connected, as long as they are in the same group, information can spread rapidly. Therefore, studying how to effectively curb the spread of negative information within a limited budget is of great practical significance.

[0003] In research on suppressing the spread of negative information, Bharathi et al. were the first to propose and demonstrate that the influence maximization problem in a competitive environment can be solved using a greedy algorithm to find a near-optimal solution. Budak et al. first proposed the rumor blocking maximization (RBM) problem, a dual problem of influence maximization (IM), which aims to minimize the spread of rumors by selecting key nodes. Newman et al. demonstrated that by removing approximately 10% of highly influential nodes in descending order, the influence of rumors on other nodes can be effectively eliminated. Furthermore, Kimura et al. proposed an algorithm that blocks key links rather than nodes to reduce the spread of rumors. These studies provide theoretical foundations and algorithmic support for suppressing the spread of negative information.

[0004] However, existing research still has several limitations. First, most studies have overlooked the impact of group structure on information dissemination. The broadcast-like nature of group dissemination makes the spread of negative information more rapid and difficult to control. Second, most existing algorithms fail to fully consider cost constraints, simply treating the selection cost of each node as equal, ignoring the cost differences caused by node characteristics. Finally, existing research is relatively simplistic in its choice of suppression strategies, often focusing solely on suppressing the spread of negative information by controlling key nodes, while ignoring other possible strategies such as group disbanding. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for maximizing the suppression of negative influence in a group network considering budget constraints, which can select the optimal suppression strategy according to the characteristics of the group and cost-effectiveness, effectively reduce the spread of negative information, and avoid unnecessary damage to the network structure.

[0006] To achieve the above object, the present invention provides a method for maximizing negative influence suppression in a group network considering budget constraints, comprising the following steps:

[0007] Step 1, establish the GIC model;

[0008] Step 2: Define cost constraints: node cost and group cost;

[0009] Step 3: Design a negative information suppression maximization algorithm that integrates multiple strategies under cost constraints: group cost-benefit, group infection rate, and group connectivity scale;

[0010] Step 4: Select a positive seed.

[0011] Compared with the existing technology, the beneficial effect of the present invention lies in that, by establishing a Group Independent Cascade Model (GIC), the information propagation dynamics under the group structure are simulated, and a Multi-Strategy Integration Algorithm for Budget-constraint Negative Information Blocking Maximization (MSI-BCIBM) is designed. By comprehensively considering factors such as cost-effectiveness, group infection rate and group connectivity scale, the optimal suppression strategy is selected, thereby effectively suppressing the spread of negative information under a limited budget, effectively reducing the spread of negative information, and avoiding unnecessary damage to the network structure.

[0012] As a further improvement of the present invention, the specific content of step 1 is as follows:

[0013] The specific contents of step 1 are as follows:

[0014] Given a group network G = (V, E, C), V represents the set of nodes, E represents the interaction relationship between nodes, and C represents the group in the network;

[0015] The goal is to select the optimal suppression strategy A for each group without exceeding the budget. * , so that the total influence of negative information in the network is minimized at the end of the propagation process, that is

[0016]

[0017] Among them, g represents the total number of groups, Represents the empty set, which is used to indicate that no suppression operation is performed. S N Represents the initial negative influence node in the network, A i represents the suppression strategy executed on the i-th group, B is the given cost budget, It is a function that represents the spread of negative information in the network under a given suppression strategy. Specifically, it calculates the number of nodes infected by negative information in the network after the propagation process is completed. Indicates that group c i When the suppression operation is performed, the number of nodes in the network infected by negative information after the propagation process is completed, Indicates that for group c i When the corresponding suppression strategy is executed, the number of nodes infected by negative information in the network after the propagation process ends, i is the number of group C, which is a natural number, c i is the i-th group.

[0018] In this way, the model can accurately capture the propagation characteristics of information within and between groups, while taking into account the probabilistic and dynamic nature of information propagation.

[0019] As a further improvement of the present invention, the details of the propagation process in step 1 are as follows:

[0020] S1, at the initial moment, only the negative information source node in the network is in a negative activation state, and the rest of the nodes are in an inactive state;

[0021] S2, at each time step, each node in a positive or negative activation state will propagate information to its direct neighbor nodes and other nodes in the group with a certain probability. After receiving the information, the node will decide whether to accept and propagate the information based on the attractiveness of the information and its own acceptance probability. In order to simulate the attractiveness of information to different nodes at different times in the network, the following function is constructed.

[0022]

[0023] Among them, A v (t,β v ) represents the attraction of information in the network to node v at time t; β v represents the education loss rate of node v. The education loss rate is used to indicate the node's tendency to accept and disseminate information. t represents the time step, which is used to simulate the time factor in the information dissemination process. According to the Ising model and Boltzmann distribution, the probability of a node in the group accepting information at this time can be obtained as follows: The formula is:

[0024]

[0025] BS i represents the information broadcast intensity of the i-th group, indicating the node's tendency to accept and spread information, x is the number of information-activated nodes in the group, indicating the number of nodes that have received the information in the group, and e is the natural index;

[0026] S3: If a node receives both positive and negative information, it will prioritize the negative information for dissemination; the dissemination process continues until no new nodes are activated in the network.

[0027] In the GIC model, nodes are divided into three states: inactive (not exposed to information), positively activated (exposed and propagating positive information), and negatively activated (exposed and propagating negative information). During information propagation, each node propagates information to its neighbors or other nodes within the group based on its state and propagation probability. The GIC model simulates the dynamics of information propagation within a group structure, providing a foundation for the subsequent selection of suppression strategies.

[0028] As a further improvement of the present invention, the specific content of defining the node cost in step 2 is as follows:

[0029] The node cost cost node (v) is set to:

[0030]

[0031] Where m, s, and r are constants, m = s = 1.1, r = 10, and d(v) is the degree of node v.

[0032] In this way, the cost of a node is related to its degree. A node with a higher degree has a greater influence in spreading information, so the cost of suppressing the node is also higher.

[0033] As a further improvement of the present invention, the specific content of defining the group cost in step 2 is as follows:

[0034] The cost of group disbanding takes into account both the size of the group and the emotional investment of group members. The larger the group size, the more damaging the network structure will be if the group is disbanded. The higher the emotional investment of group members, the greater the impact of disbanding the group on the members.

[0035] In summary, group c i Dissolution cost group (c i )for:

[0036] cost group (c i )=|V i|·Inv i (5)

[0037] where c i ∈C represents a group in the group set C, |V i | indicates group c i The number of all nodes in Inv i Indicates group c i The emotional investment of each member in the game is as follows:

[0038]

[0039] Among them E i Indicates group c i All the edges in V i Indicates group c i For all nodes in |u∩V j | indicates group c i Are other nodes u except node v in other groups c? j middle.

[0040] Thus, the first half of formula (6) uses the number of edges within a group and the degree of the nodes within the group to measure the proportion of the number of relationships within the entire group to all the social relationships of the group members. The second half evaluates the average number of group members participating in the group. These two sets of relationships can be used to quantify the importance of the group to its members. By defining the costs of nodes and groups, the optimal suppression strategy can be selected within the budget constraint, ensuring the suppression effect while avoiding unnecessary cost waste.

[0041] As a further improvement of the present invention, the specific contents of the group cost-benefit in step 3 are as follows:

[0042] According to the three-degree influence principle and the attenuation of information attraction, most of the influence of the negative information source node should be limited to the nodes it can reach in two time steps. Therefore, the neighbors directly connected to the negative information source node s The group c where the source node s is located i ,Neighbor Group c j The sum of the activation probabilities of the nodes in the group is taken as the i The degree of harm to the network can be expressed in the form of:

[0043]

[0044] Where s∈(S N ∩V i ), j≠i, and Represent the source node s and direct neighbors respectively The probability of node v being activated in the same group represents the probability of group c being activated in the first time step i The degree of harm to the network, the second time step group c i The degree of harm to the network can be determined by the activation probability of the two-hop neighbors of the source node s Probability of secondary broadcast activation within the group and adjacent group information broadcast activation probability Get; V i is defined as the set of all nodes in the i-th group, |V i | is the number of all nodes in the i-th group;

[0045] Then group c i Cost-benefit CE i for:

[0046] CE i =Inf i / cost group (i)#(8). The cost-effectiveness is measured by the ratio of the harm the group causes to the network to the cost of disbanding the group.

[0047] As a further improvement of the present invention, the specific content of the group infection rate in step 3 is as follows:

[0048] Group infection rate IR i Indicates group c i The number of nodes expected to be infected in group c i The ratio of the total number of nodes, that is:

[0049]

[0050] The denominator in this formula is group c i The number of nodes, the numerator is the sum of the activation probabilities of the direct neighbors and the same group nodes of the negative information source node.

[0051] The infection rate of such a group represents the ratio of the number of nodes expected to be infected in the group to the total number of nodes in the group.

[0052] As a further improvement of the present invention, the specific content of the group connectivity scale in step 3 is as follows:

[0053] The group connectivity scale indicates the ratio of the number of nodes in the group and connected groups to the total number of nodes in the network, reflecting the influence of the group. It can be formally expressed as

[0054]

[0055] In this formula, |V i | represents the number of nodes in the i-th group, represents the sum of the number of nodes in group j that have outgoing edge connections to group i, |V| represents the total number of nodes in the entire network, and outgoing edge connections indicate that group i is an adjacent group of these groups; |V j | represents the number of nodes in the jth group, V j represents the set of nodes in the jth group, c j is the j-th group, j≠i.

[0056] The connectivity scale thus represents the ratio of the number of nodes in a group and its connected groups to the total number of nodes in the network.

[0057] As a further improvement of the present invention, the specific contents of step 4 are as follows:

[0058] Step 4.1, Initialization: Count the number of groups participated by all nodes in the group and record the number of groups participated by each node;

[0059] Step 4.2, select positive seeds: select the node with the most participation in the group as the positive seed; if there are multiple nodes with the same number of participation in the group, select the node with the highest degree as the positive seed;

[0060] Step 4.3, update the group status: mark the selected positive seed node as positively activated and update the status of its neighbor nodes; the positive seed node will propagate positive information to its neighbor nodes and other nodes in the group with a certain probability;

[0061] Step 4.4, repeat selection: If there are still nodes in the group that have not been activated, repeat the above process of selecting positive seeds until all nodes in the group are activated or the budget is exhausted.

[0062] By combining steps 3 and 4, we can maximize the spread of positive information and effectively suppress the spread of negative information by disbanding groups and selecting appropriate positive seed sets (selecting the nodes with the most participation in the group as positive seeds) according to the specific circumstances of different groups in the network. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 This is a flow chart of the MSI-BCIBM algorithm in the present invention.

[0064] Figure 2 This is the framework diagram of the MSI-BCIBM algorithm in the present invention.

[0065] Figure 3 This is a heat map of the effect of setting the MSI-BCIBM threshold in the present invention.

[0066] Figure 4 This is a comparison chart of the inhibition strategies in the present invention.

[0067] Figure 5 It is a comparison diagram of the inhibitory effect in the present invention. DETAILED DESCRIPTION

[0068] The present invention will be further described below in conjunction with the accompanying drawings:

[0069] like Figure 1-2 The method for maximizing negative influence suppression in a group network considering budget constraints shown in FIG. includes the following steps:

[0070] Step 1, establish the GIC model;

[0071] Given a group network G = (V, E, C), V represents the set of nodes, E represents the interaction relationship between nodes, and C represents the group in the network;

[0072] The goal is to select the optimal suppression strategy A for each group without exceeding the budget. * , so that the total influence of negative information in the network is minimized at the end of the propagation process, that is

[0073]

[0074] Among them, g represents the total number of groups, Represents the empty set, which is used to indicate that no suppression operation is performed. S N Represents the initial negative influence node in the network, A i represents the suppression strategy executed on the i-th group, B is the given cost budget, It is a function that represents the spread of negative information in the network under a given suppression strategy. Specifically, it calculates the number of nodes infected by negative information in the network after the propagation process is completed. Indicates that group c i When the suppression operation is performed, the number of nodes in the network infected by negative information after the propagation process is completed, Indicates that for group c i When the corresponding suppression strategy is executed, the number of nodes infected by negative information in the network after the propagation process ends, i is the number of group C, which is a natural number, c i is the i-th group.

[0075] The details of the propagation process in step 1 are as follows:

[0076] S1, at the initial moment, only the negative information source node in the network is in a negative activation state, and the rest of the nodes are in an inactive state;

[0077] S2, at each time step, each node in a positive or negative activation state will propagate information to its direct neighbor nodes and other nodes in the group with a certain probability. After receiving the information, the node will decide whether to accept and propagate the information based on the attractiveness of the information and its own acceptance probability. In order to simulate the attractiveness of information to different nodes at different times in the network, the following function is constructed.

[0078]

[0079] Among them, A v (t,β v ) represents the attraction of information in the network to node v at time t; β v represents the education loss rate of node v. The education loss rate is used to indicate the node's tendency to accept and disseminate information. t represents the time step, which is used to simulate the time factor in the information dissemination process. According to the Ising model and Boltzmann distribution, the probability of a node in the group accepting information at this time can be obtained as follows: The formula is:

[0080]

[0081] BS i represents the information broadcast intensity of the i-th group, indicating the node's tendency to accept and spread information, x is the number of information-activated nodes in the group, indicating the number of nodes that have received the information in the group, and e is the natural index;

[0082] S3: If a node receives both positive and negative information, it will prioritize the negative information for dissemination; the dissemination process continues until no new nodes are activated in the network.

[0083] Step 2: Define cost constraints: node cost and group cost;

[0084] The specific content of defining node cost in step 2 is as follows,

[0085] The node cost cost node (v) is set to:

[0086]

[0087] Where m, s, and r are constants, m = s = 1.1, r = 10, and d(v) is the degree of node v.

[0088] The specific content of defining the group cost in step 2 is as follows,

[0089] The cost of group disbanding takes into account both the size of the group and the emotional investment of group members. The larger the group size, the more damaging the network structure will be if the group is disbanded. The higher the emotional investment of group members, the greater the impact of disbanding the group on the members.

[0090] In summary, group c i Dissolution cost group (c i )for:

[0091] cost group (c i )=|V i |·Inv i (5)

[0092] where c i ∈C represents a group in the group set C, |V i | indicates group c i The number of all nodes in Inv i Indicates group c i The emotional investment of each member in the game is as follows:

[0093]

[0094] Among them E i Indicates group c i All the edges in V i Indicates group c i For all nodes in |u∩V j | indicates group c i Are other nodes u except node v in other groups c? j middle.

[0095] Step 3: Design a negative information suppression maximization algorithm that integrates multiple strategies under cost constraints: group cost-benefit, group infection rate, and group connectivity scale;

[0096] According to the three-degree influence principle and the attenuation of information attraction, most of the influence of the negative information source node should be limited to the nodes it can reach in two time steps. Therefore, the neighbors directly connected to the negative information source node s The group c where the source node s is located i ,Neighbor Group c j The sum of the activation probabilities of the nodes in the group is taken as the i The degree of harm to the network can be expressed in the form of:

[0097]

[0098] Where s∈(S N ∩Vi ), j≠i, and Represent the source node s and direct neighbors respectively The probability of node v being activated in the same group represents the probability of group c being activated in the first time step i The degree of harm to the network, the second time step group c i The degree of harm to the network can be determined by the activation probability of the two-hop neighbors of the source node s Probability of secondary broadcast activation within the group and adjacent group information broadcast activation probability Get; V i is defined as the set of all nodes in the i-th group, |V i | is the number of all nodes in the i-th group;

[0099] Then group c i Cost-benefit CE i for:

[0100] CE i =Inf i / cost group (i) (8)

[0101] The specific content of the group infection rate in step 3 is as follows:

[0102] Group infection rate IR i Indicates group c i The number of nodes expected to be infected in group c i The ratio of the total number of nodes, that is:

[0103]

[0104] The denominator in this formula is group c i The number of nodes, the numerator is the sum of the activation probabilities of the direct neighbors and the same group nodes of the negative information source node.

[0105] The specific content of the group connectivity scale in step 3 is as follows:

[0106] The group connectivity scale indicates the ratio of the number of nodes in the group and connected groups to the total number of nodes in the network, reflecting the influence of the group. It can be formally expressed as

[0107]

[0108] In this formula, |V i | represents the number of nodes in the i-th group, represents the sum of the number of nodes in group j that have outgoing edge connections to group i, |V| represents the total number of nodes in the entire network, and outgoing edge connections indicate that group i is an adjacent group of these groups; |V j | represents the number of nodes in the jth group, V j represents the set of nodes in the jth group, c j is the j-th group, j≠i.

[0109] Step 4: Select a positive seed.

[0110] Step 4.1, Initialization: Count the number of groups participated by all nodes in the group and record the number of groups participated by each node;

[0111] Step 4.2, select positive seeds: select the node with the most participation in the group as the positive seed; if there are multiple nodes with the same number of participation in the group, select the node with the highest degree as the positive seed;

[0112] Step 4.3, update the group status: mark the selected positive seed node as positively activated and update the status of its neighbor nodes; the positive seed node will propagate positive information to its neighbor nodes and other nodes in the group with a certain probability;

[0113] Step 4.4, repeat selection: If there are still nodes in the group that have not been activated, repeat the above process of selecting positive seeds until all nodes in the group are activated or the budget is exhausted.

[0114] This paper establishes a Group Independent Cascade Model (GIC) to simulate the dynamics of information propagation in a group structure and proposes a Multi-Strategy Integration Algorithm for Budget-constraint Negative Information Blocking Maximization (MSI-BCIBM). This algorithm selects the optimal suppression strategy based on the group's characteristics and cost-effectiveness, effectively reducing the spread of negative information while avoiding unnecessary damage to the network structure.

[0115] The core of the present invention is to minimize the spread of negative information in a group network under budget constraints through a comprehensive algorithm. The algorithm first establishes a GIC model to accurately simulate the propagation dynamics of information under a group structure and capture the propagation characteristics of information within and between groups. On this basis, the present invention introduces a cost constraint mechanism to allocate a reasonable cost to each group and node, ensuring that the selection of suppression strategies not only considers the effect but also takes into account cost-effectiveness. The MSI-BCIBM algorithm can comprehensively evaluate the infection rate, connectivity scale and cost-effectiveness of the group and dynamically select the optimal suppression strategy, including disbanding the group or selecting positive seeds to spread positive information.

[0116] In order to simulate the propagation dynamics of information under a group structure, the present invention establishes a GIC model. This model can accurately capture the propagation characteristics of information within and between groups, while taking into account the probabilistic and dynamic nature of information propagation. In the GIC model, nodes are divided into three states: an unactivated state (no contact with information), a positively activated state (contacted and propagated positive information), and a negatively activated state (contacted and propagated negative information). During the information propagation process, each node propagates information to its neighboring nodes or other nodes in the group based on its state and propagation probability. Through the GIC model, the present invention can simulate the propagation dynamics of information under a group structure, providing a basis for the subsequent selection of suppression strategies.

[0117] In order to ensure that the selection of suppression strategies not only considers the effect but also takes into account cost-effectiveness, the present invention sets the cost of suppression for all nodes and groups in the network. It includes (1) node cost: the cost of a node is related to its degree. The higher the degree of a node, the greater its influence in spreading information, so the cost of suppressing the node is also higher; (2) group cost: the cost of disbanding a group takes into account the size of the group and the emotional investment of group members. The larger the group size, the greater the damage to the network structure caused by disbanding the group; the higher the emotional investment of group members, the greater the impact of disbanding the group on the members. The first half of formula (6) uses the number of edges within the group and the degree of the nodes in the group to measure the proportion of the number of relationships within the entire group to all the social relationships of the group members, and the second half evaluates the average number of group members participating in the group. Through these two sets of relationships, the importance of the group to the members in the group can be quantified. By defining the cost of nodes and groups, the present invention can select the optimal suppression strategy under budget constraints, ensuring the suppression effect while avoiding unnecessary cost waste.

[0118] The specific application of the MSI-BCIBM algorithm is as follows:

[0119] (1) Pre-allocation suppression strategy: For groups with negative information sources, the initial strategy is to disband the group. This is because the presence of negative information source nodes will significantly increase the risk of information dissemination within the group, and disbanding the group can effectively cut off the propagation path of negative information.

[0120] (2) Calculate cost-effectiveness: Evaluate each group's suppression strategy based on its infection rate, connectivity scale, and cost-effectiveness. The infection rate of a group represents the ratio of the number of nodes expected to be infected to the total number of nodes in the group, and the connectivity scale represents the ratio of the number of nodes in the group and its connected groups to the total number of nodes in the network. Cost-effectiveness is measured by the ratio of the group's harm to the network to the cost of disbanding the group.

[0121] (3) Optimize the suppression strategy: For groups with high cost-benefit, decide whether to disband the group or select positive seeds to spread positive information based on the group infection rate and connectivity scale. If both the group infection rate and connectivity scale are greater than the set threshold, maintain the strategy of disbanding the group; otherwise, adjust to the strategy of selecting positive seeds to spread positive information.

[0122] (4) Selecting positive seeds: For groups that do not need to be disbanded, a heuristic algorithm is used to select the nodes that participate in the group the most as positive seeds. This algorithm selects the nodes that participate in the group the most as positive seeds to maximize the spread of positive information and further suppress the spread of negative information.

[0123] Through this multi-strategy fusion algorithm, the present invention can dynamically select the optimal suppression strategy based on the characteristics and cost-effectiveness of the group containing negative information within a limited budget, effectively reducing the spread of negative information while avoiding unnecessary damage to the network structure.

[0124] In order to verify the effectiveness of the cost-constrained maximization algorithm for suppressing negative information in group networks (MSI-BCIBM), we conducted extensive experiments on four real-world datasets (Ego-Facebook, Email-Eu-Core, sinaNet, and MSRC-21C). Figure 3 The suppression effect of the MSI-BCIBM algorithm under different group infection rate thresholds δ and group connectivity scale thresholds γ was studied. Figure 4 The suppression effect of the MSI-BCIBM algorithm was compared with that of the algorithm using a single strategy (only disbanding the group or only selecting positive seeds). Figure 5 The proposed MSI-BCIBM algorithm is compared with five existing algorithms (Degree, Source-BC, PWD, SGDA, and SGEA). All algorithms are evaluated under the GIC model, where the propagation probability is calculated based on the connection strength and interest similarity of the nodes.

[0125] Figure 3This figure shows the suppression effect of the MSI-BCIBM algorithm under different group infection rate thresholds δ and group connectivity thresholds γ. In the heat map, colors closer to dark blue indicate better suppression effects under that parameter combination, while colors closer to red indicate worse suppression effects under that parameter combination. Figure 3 (a) is the result of the algorithm in the Ego-Facebook dataset. The figure shows that the algorithm has a better suppression effect when the algorithm parameters are δ∈[0.07,0.08]. Figure 3 (b) is the result of the algorithm in the Ego-Facebook dataset. The figure shows that the algorithm has a better suppression effect when the algorithm parameters are δ∈[0.07,0.08] and γ∈[0.3,0.6]. Figure 3 (c) is the result of the algorithm in the sinaNet dataset. The figure shows that the algorithm has the best suppression effect when the algorithm parameters are δ=0.08 and γ=0.6. Figure 3 (d) shows the algorithm's results on the MSRC-21C dataset. The figure shows that the algorithm achieves the best suppression effect when the algorithm parameters are set to δ = 0.09 and γ = 0.5. Experimental results show that the algorithm parameters are sensitive to the dataset. Overall, the algorithm achieves the best suppression effect when the algorithm parameters are set to δ = 0.08 and γ = 0.6. Reasonable threshold settings can significantly improve the suppression effect.

[0126] Figure 4 The comparison of the suppression effect of the MSI-BCIBM algorithm and the algorithm using a single strategy (disbanding the group only or selecting only positive seeds) is shown. The lower the bar graph, the better the suppression effect of the scheme, and the higher the bar graph, the worse the suppression effect of the strategy. Figure 4 (a) is the result of the algorithm in the Ego-Facebook dataset. The figure shows that as the budget increases, the suppression effect of the three strategies is improved. In most cases, the MSI-BCIBM algorithm always performs best. Figure 4 (b) is the result of the algorithm in the Ego-Facebook dataset. The figure shows that as the budget increases, the suppression effect of the three strategies is improved, and the effect of the MSI-BCIBM algorithm is always better than other strategies. Figure 4 (c) is the result of the algorithm in the sinaNet dataset. The figure shows that with the increase of budget, the suppression effect of the three strategies is improved, and the suppression effect of the MSI-BCIBM algorithm is the most obvious, significantly better than other strategies. Figure 4(d) shows the algorithm's results on the MSRC-21C dataset. The figure shows that as the budget increases, the suppression effectiveness of the three strategies improves. In most cases, the MSI-BCIBM algorithm achieves the best suppression effect. Experimental results demonstrate that the MSI-BCIBM algorithm outperforms single-strategy algorithms at most budget levels, demonstrating that in complex network structures, the fusion of multiple suppression strategies can better leverage network characteristics and achieve superior suppression results.

[0127] Figure 5 This chart compares the suppression performance of the MSI-BCIBM algorithm with five existing algorithms on different datasets. Lower values in the line graph indicate better suppression performance, while higher values indicate worse performance. Figure 5 (a)-(d) show the performance of each algorithm on the Ego-Facebook dataset, Email-Eu-Core dataset, SinaNet dataset, and MSRC-21C dataset, respectively. It can be seen that the suppression effect of each algorithm improves with increasing budget. When the budget is greater than 0.4, the MSI-BCIBM algorithm outperforms all other algorithms. This demonstrates that the MSI-BCIBM algorithm can better adapt to different network structures and scales, achieving more effective negative information suppression.

[0128] The present invention simulates the dynamics of information propagation under a group structure by establishing a GIC model, and proposes a negative information suppression maximization algorithm that integrates multiple strategies under cost constraints. It can select the optimal suppression strategy based on the characteristics of the group and cost-effectiveness. Under a limited budget, the present invention can effectively reduce the spread of negative information while avoiding unnecessary damage to the network structure. Through experimental verification on multiple real-world data sets, the algorithm of the present invention has shown significant performance advantages in suppressing the spread of negative information, proving that the suppression effect of combining multiple strategies is better than that of a single strategy, providing a new idea and algorithm for solving the problem of suppressing the spread of negative information under a group structure.

[0129] The present invention is not limited to the above-mentioned embodiments. On the basis of the technical solution disclosed herein, those skilled in the art can make some substitutions and modifications to some of the technical features therein according to the disclosed technical content without creative labor, and these substitutions and modifications are all within the protection scope of the present invention.

Claims

1. A method for maximizing negative influence suppression in a group network considering budget constraints, characterized by: The following steps are included: Step 1, establish the GIC model; Step 2: Define cost constraints: node cost and group cost; Step 3: Design a negative information suppression maximization algorithm that integrates multiple strategies under cost constraints: group cost-benefit, group infection rate, and group connectivity scale; Step 4: Select a positive seed.

2. The method for maximizing negative influence suppression in a group network considering budget constraints according to claim 1, characterized in that: The specific contents of step 1 are as follows: Given a group network G = (V, E, C), V represents the set of nodes, E represents the interaction relationship between nodes, and C represents the group in the network; The goal is to select the optimal suppression strategy A for each group without exceeding the budget. * , so that the total influence of negative information in the network is minimized at the end of the propagation process, that is Among them, g represents the total number of groups, Represents the empty set, which is used to indicate that no suppression operation is performed. S N Represents the initial negative influence node in the network, A i represents the suppression strategy executed on the i-th group, B is the given cost budget, It is a function that represents the spread of negative information in the network under a given suppression strategy. Specifically, it calculates the number of nodes infected by negative information in the network after the propagation process is completed. Indicates that group c i When the suppression operation is performed, the number of nodes in the network infected by negative information after the propagation process is completed, Indicates that for group c i When the corresponding suppression strategy is executed, the number of nodes infected by negative information in the network after the propagation process ends, i is the number of group C, which is a natural number, c i is the i-th group.

3. The method for maximizing negative influence suppression in a group network considering budget constraints according to claim 2, characterized in that: The details of the propagation process in step 1 are as follows: S1, at the initial moment, only the negative information source node in the network is in a negative activation state, and the rest of the nodes are in an inactive state; S2, at each time step, each node in a positive or negative activation state will propagate information to its direct neighbor nodes and other nodes in the group with a certain probability. After receiving the information, the node will decide whether to accept and propagate the information based on the attractiveness of the information and its own acceptance probability. In order to simulate the attractiveness of information to different nodes at different times in the network, the following function is constructed. Among them, A v (t,β v ) represents the attraction of information in the network to node v at time t; β v represents the education loss rate of node v. The education loss rate is used to indicate the node's tendency to accept and disseminate information. t represents the time step, which is used to simulate the time factor in the information dissemination process. According to the Ising model and Boltzmann distribution, the probability of a node in the group accepting information at this time can be obtained as follows: The formula is: BS i represents the information broadcast intensity of the i-th group, indicating the node's tendency to accept and spread information, x is the number of information-activated nodes in the group, indicating the number of nodes that have received the information in the group, and e is the natural index; S3: If a node receives both positive and negative information, it will prioritize the negative information for dissemination; the dissemination process continues until no new nodes are activated in the network.

4. The method for maximizing negative influence suppression in a group network considering budget constraints according to claim 3, characterized in that: The specific content of defining node cost in step 2 is as follows, The node cost cost node (v) is set to: Where m, s, and r are constants, m = s = 1.1, r = 10, and d(v) is the degree of node v.

5. The method for maximizing negative influence suppression in a group network considering budget constraints according to claim 4, characterized in that: The specific content of defining the group cost in step 2 is as follows, The cost of group disbanding takes into account both the size of the group and the emotional investment of group members. The larger the group size, the more damaging the network structure will be if the group is disbanded. The higher the emotional investment of group members, the greater the impact of disbanding the group on the members. In summary, group c i Dissolution cost group (c i )for: cost group (c i )=|V i |·Inv i (5) where c i ∈C represents a group in the group set C, |V i | indicates group c i The number of all nodes in Inv i Indicates group c i The emotional investment of each member in the game is as follows: Among them E i Indicates group c i All the edges in V i Indicates group c i For all nodes in |u∩V j | indicates group c i Are other nodes u except node v in other groups c? j middle.

6. The method for maximizing negative influence suppression in a group network considering budget constraints according to claim 5, characterized in that: The specific contents of the group cost-benefit in step 3 are as follows: According to the three-degree influence principle and the attenuation of information attraction, most of the influence of the negative information source node should be limited to the nodes it can reach in two time steps. Therefore, the neighbors directly connected to the negative information source node s The group c where the source node s is located i ,Neighbor Group c j The sum of the activation probabilities of the nodes in the group is taken as the i The degree of harm to the network can be expressed in the form of: Where s∈(S N ∩V i ), j≠i, and Represent the source node s and direct neighbors respectively The probability of node v being activated in the same group represents the probability of group c being activated in the first time step i The degree of harm to the network, the second time step group c i The degree of harm to the network can be determined by the activation probability of the two-hop neighbors of the source node s Probability of secondary broadcast activation within the group and adjacent group information broadcast activation probability Get; V i is defined as the set of all nodes in the i-th group, |V i | is the number of all nodes in the i-th group; Then group c i Cost-benefit CE i for: WHAT i =Inf i / cost group (i) (8).

7. The method for maximizing negative influence suppression in a group network considering budget constraints according to claim 6, characterized in that: The specific content of the group infection rate in step 3 is as follows: Group infection rate IR i Indicates group c i The number of nodes expected to be infected in group c i The ratio of the total number of nodes, that is: The denominator in this formula is group c i The number of nodes, the numerator is the sum of the activation probabilities of the direct neighbors and the same group nodes of the negative information source node.

8. The method for maximizing negative influence suppression in a group network considering budget constraints according to claim 7, characterized in that: The specific content of the group connectivity scale in step 3 is as follows: The group connectivity scale indicates the ratio of the number of nodes in the group and connected groups to the total number of nodes in the network, reflecting the influence of the group. It can be formally expressed as In this formula, |V i | represents the number of nodes in the i-th group, represents the sum of the number of nodes in group j that have outgoing edge connections to group i, |V| represents the total number of nodes in the entire network, and outgoing edge connections indicate that group i is an adjacent group of these groups; |V j | represents the number of nodes in the jth group, V j represents the set of nodes in the jth group, c j is the j-th group, j≠i.

9. The method for maximizing negative influence suppression in a group network considering budget constraints according to claim 8, characterized in that: The specific contents of step 4 are as follows: Step 4.1, initialization: count the number of groups participated by all nodes in the group and record the number of groups participated by each node; Step 4.2, select positive seeds: select the node with the most participation in the group as the positive seed; if there are multiple nodes with the same number of participation in the group, select the node with the highest degree as the positive seed; Step 4.3, update the group status: mark the selected positive seed node as positively activated and update the status of its neighbor nodes; the positive seed node will propagate positive information to its neighbor nodes and other nodes in the group with a certain probability; Step 4.4, repeat selection: If there are still nodes in the group that have not been activated, repeat the above process of selecting positive seeds until all nodes in the group are activated or the budget is exhausted.

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